Numerical Growth of the Projective Diameter Proxy Near the Mixing Boundary for Twisted Bird–Map Operators (Paper 42 in the Non-Holomorphic Fractal Series)

Paper 42 in the Non-Holomorphic Fractal Series. Paper 41 defined a Hilbert projective-diameter proxy D(h, ε) on the certified Ulam grid and reported its values on the coarse nine-point grid E_wide for all three kernels. In this paper we refine the ε-grid near the mixing boundary (around 0.70 and 1.10) and quantify how D(h, ε) behaves on the boundary subgrid E_bdy = {0.70, 0.72, 0.74, 0.76, 0.78, 1.02, 1.05, 1.07, 1.08, 1.10}. Using the same enriched six-vector test family and the same certified Ulam infrastructure as Paper 41, we find: (i) the WBA and alien kernels show D(h, ε) ≥ D_core + δ(ε) uniformly on E_bdy with δ(ε) > 0 increasing as ε approaches the boundary endpoints; (ii) the Lorentzian kernel exhibits D(h, ε) < D_core throughout E_bdy but with a clear increasing trend toward 1.10; and (iii) no dramatic numerical blow-up is observed on this discrete subgrid. These findings are purely diagnostic and numerical; they sharpen the boundary obstruction of Paper 40 but introduce no new Ulam computations, kernels, or analytic hypotheses.